Problem: Solve for $c$. Give an exact answer. $0.2(10-5c)=5c-16$ $c =$
Explanation: We need to manipulate the equation to get $ c $ by itself. $\begin{aligned} 0.2(10-5c) &= 5c-16 \\\\ 2-c &= 5c-16~~~~~~~~~~\gray{\text{Distribute}}\\\\ 2-c{-5c} &= 5c-16{-5c} ~~~~~~~~~~\gray{\text{Subtract 5c from each side}}\\\\ 2-6c &= -16~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2-6c{-2} &= -16{-2} ~~~~~~~~~~\gray{\text{Subtract 2 from each side}}\\\\ -6c&=-18 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{-6c}{{-6}}&= \dfrac{-18}{{-6}}~~~~~~~~~~\gray{\text{Divide each side by -6}} \\\\ c &= {3} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ c = { 3 }~~~~~~~~$ [Let's check our work!]